Ishaan is 16 years older than Daniel. Nine years ago, Ishaan was 3 times as old as Daniel. How old is Daniel now?
Solution: We can use the given information to write down two equations that describe the ages of Ishaan and Daniel. Let Ishaan's current age be $i$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $i = d + 16$ Nine years ago, Ishaan was $i - 9$ years old, and Daniel was $d - 9$ years old. The information in the second sentence can be expressed in the following equation: $i - 9 = 3(d - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to use our first equation for $i$ and substitute it into our second equation. Our first equation is: $i = d + 16$ . Substituting this into our second equation, we get the equation: $(d + 16)$ $-$ $9 = 3(d - 9)$ which combines the information about $d$ from both of our original equations. Simplifying both sides of this equation, we get: $d + 7 = 3 d - 27$ Solving for $d$ , we get: $2 d = 34$ $d = 17$.